Mean values of observables of infinite-particle systems

We study the existence of mean values of observables for infinite-particle systems. Using solutions of the initial value problems to the BBGKY hierarchy and to its dual, we prove the local, in time, existence of the mean value functionals in the cases where either observables or states vary in time. We also discuss problems on the existence of such functionals for several different classes of observables and for an arbitrary time interval. Additional information and comments: Key words: infinite-particle systems; BBGKY hierarchy; dual BBGKY hierarchy; cumulant (semi-invariant); mean values of observables.